Is my working of this problem ok?

f:N->R

f(n) =

prove f(n) = O(n) < - - - thats big O with a "-" in it

= since each term is >=0

<= since log2n<=n

<= since n>=1

=

=

=3n

since each term >= 0

>= since log2n is >= 0 for n>=1

=

=n

Therfore

f(n) = O(n)

I really hope i am doing this correctly

Thanks for any help and input.